Fast Calculations for the Magnetohydrodynamic Flow and Heat Transfer of Bingham Fluids with the Hall Effect

Abstract

This study examines a mathematical model to represent the magnetohydrodynamic flow and heat transfer of Bingham fluids. The model is subject to a magnetic field’s influence and incorporates the modified energy equation derived from Fourier’s law. For numerical computation, we utilize the spectral collocation method in conjunction with the $L1$ algorithm to address this model. To minimize computational expenses, the sum-of-exponential technology is applied to efficiently solve the time-fractional coupled model. A specific example is provided to demonstrate the numerical method’s stability and the fast method’s efficiency. The results indicate that the numerical method converges with an accuracy of $O(\tau +N^{-r})$, and the fast method is highly effective in reducing computation times. Moreover, the parameters’ impacts on velocity and temperature are presented and discussed graphically. It is evident that as the Hall parameter increases, the peak velocity increases and the amplitude of temperature fluctuations gradually increases, although the peak temperature decreases. The Brinkman number has a significant impact on the heat transfer rate. Meanwhile, as the Hartmann number increases, the inhibitory effect of the magnetic field on the flow is amplified.